An approximation scheme for the time fractional convection-diffusion equation

被引：33

作者：

Zhang, Juan ^{[1
]}

Zhang, Xindong ^{[1
]}

Yang, Bohui ^{[1
]}

机构：

[1] Xinjiang Normal Univ, Coll Math Sci, Urumqi 830017, Xinjiang, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2018年 / 335卷

关键词：

Time fractional convection-diffusion equation; Caputo derivative; Stability; Convergence; Finite difference method; FINITE-ELEMENT-METHOD; PARTIAL-DIFFERENTIAL-EQUATION; NONLINEAR SOURCE-TERM; SPACE;

D O I：

10.1016/j.amc.2018.04.019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a discrete form is proposed for solving time fractional convection-diffusion equation. Firstly, we obtain a time discrete scheme based on finite difference method. Secondly, we prove that the time discrete scheme is unconditionally stable, and the numerical solution converges to the exact one with order O(tau(2-infinity)), where tau is the time step size. Finally, two numerical examples are proposed respectively, to verify the order of convergence. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：305 / 312

页数：8

共 50 条

[21] DOUBLE EXPONENTIAL EULER SINC COLLOCATION METHOD FOR A TIME-FRACTIONAL CONVECTION-DIFFUSION EQUATION
Eftekhari, Ali
FACTA UNIVERSITATIS-SERIES MATHEMATICS AND INFORMATICS, 2019, 34 (04): : 745 - 753
[22] A high-order numerical scheme for multidimensional convection-diffusion-reaction equation with time-fractional derivative
Ngondiep, Eric
NUMERICAL ALGORITHMS, 2023, 94 (02) : 681 - 700
[23] Linearized Crank-Nicolson Scheme for the Two-Dimensional Nonlinear Riesz Space-Fractional Convection-Diffusion Equation
Basha, Merfat
Anley, Eyaya Fekadie
Dai, Binxiang
FRACTAL AND FRACTIONAL, 2023, 7 (03)
[24] An implicit difference scheme with the KPS preconditioner for two-dimensional time-space fractional convection-diffusion equations
Zhou, Yongtao
Zhang, Chengjian
Brugnano, Luigi
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2020, 80 (01) : 31 - 42
[25] Numerical solution of time-fractional singularly perturbed convection-diffusion problems with a delay in time
Kumar, Kamalesh
Chakravarthy, Pramod P.
Vigo-Aguiar, J.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (04) : 3080 - 3097
[26] Stability Analysis of a Finite Difference Scheme for a Nonlinear Time Fractional Convection Diffusion Equation
Acosta, Carlos D.
Amador, Pedro A.
Mejia, Carlos E.
ANALYSIS, MODELLING, OPTIMIZATION, AND NUMERICAL TECHNIQUES, 2015, 121 : 139 - 150
[27] Application of the operational matrix of fractional-order Legendre functions for solving the time-fractional convection-diffusion equation
Abbasbandy, Saeid
Kazem, Saeed
Alhuthali, Mohammed S.
Alsulami, Hamed H.
APPLIED MATHEMATICS AND COMPUTATION, 2015, 266 : 31 - 40
[28] Finite integration method with RBFs for solving time-fractional convection-diffusion equation with variable coefficients
Biazar, Jafar
Asadi, Mohammad Ali
COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, 2019, 7 (01): : 1 - 15
[29] A high-order exponential ADI scheme for two dimensional time fractional convection-diffusion equations
Wang, Zhibo
Vong, Seakweng
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2014, 68 (03) : 185 - 196
[30] DISCONTINUOUS GALERKIN METHOD FOR FRACTIONAL CONVECTION-DIFFUSION EQUATIONS
Xu, Qinwu
Hesthaven, Jan S.
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2014, 52 (01) : 405 - 423

← 1 2 3 4 5 →